PROBABILITY -02-ASSIGNMENT-PART-1

1. Two coins are tossed. Let A be the event that the first coin shows head and B be the event that the second coin shows a tail. Two events A and B are (a) Mutually exclusive (b) Dependent (c) Independent and mutually exclusive (d) None of these 2. A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and = card is ace of diamond, then events A and B are (a) Independent (b) Mutually exclusive (c) Dependent (d) Equally likely 3. The probabilities of three mutually exclusive events are , 1/4 and 1/6. The statement is (a) True (b) False (c) Could be either (d) Do not know 4. If , where c stands for complement, then the events and are (a) Mutually exclusive (b) Independent (c) Equally likely (d) None of these 5. If and are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is (a) [0, 1] (b) (c) (d) 6. The event A is independent of itself if and only if (a) 0 (b) 1 (c) 0, 1 (d) None of these 7. If A and B are independent events and , then (a) A and C are independent (b) B and C are independent (c) A, B and C are independent (d) All of these 8. The probability that an ordinary or a non-leap year has 53 Sundays, is (a) 2/7 (b) 1/7 (c) 3/7 (d) None of these 9. Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to (a) 1/27 (b) 1/9 (c) 4/27 (d) 1/6 10. The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is (a) (b) (c) (d) 11. In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89 is (a) 2/801 (b) 2/623 (c) 1/267 (d) 1/623 12. Two numbers are selected randomly from the set without replacement one by one. The probability that minimum of the two numbers is less than 4 is (a) 1/15 (b) 14/15 (c) 1/5 (d) 4/5 13. Among 15 players, 8 are batsmen and 7 are bowlers. Find the probability that a team is chosen of 6 batsmen and 5 bowlers (a) (b) (c) (d) None of these 14. The probability of obtaining sum ‘8’ in a single throw of two dice (a) (b) (c) (d) 15. Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is (a) (b) (c) (d) None of these 16. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is (a) (b) (c) (d) None of these 17. A bag contains 5 white, 7 black and 4 red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white, is (a) (b) (c) (d) 18. Two dice are thrown together. The probability that at least one will show its digit 6 is (a) (b) (c) (d) 19. The sum of two positive numbers is 100. The probability that their product is greater than 1000 is (a) 7/9 (b) 7/10 (c) 2/5 (d) None of these 20. Two integers are chosen at random and multiplied. The probability that the product is an even integer is (a) 1/2 (b) 2/3 (c) 3/4 (d) 4/5 21. A pair of a dice thrown, if 5 appears on at least one of the dice, then the probability that the sum is 10 or greater is (a) (b) (c) (d) 22. Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is (a) 1/34 (b) 1/35 (c) 1/17 (d) 1/68 23. If two dice are thrown simultaneously then probability that 1 comes on first dice is (a) 1/36 (b) 5/36 (c) 1/6 (d) None of these 24. Out of 30 consecutive numbers, 2 are chosen at random. The probability that their sum is odd, is (a) (b) (c) (d) 25. Three integers are chosen at random from the first 20 integers. The probability that their product is even, is (a) (b) (c) (d) 26. Two dice are thrown. The probability that the sum of the points on two dice will be 7, is (a) (b) (c) (d) 27. A bag contains tickets numbered from 1 to 20. Two tickets are drawn. The probability that both the numbers are prime, is (a) (b) (c) (d) None of these 28. In a single throw of two dice, the probability of getting more than 7 is (a) (b) (c) (d) 29. If two balanced dice are tossed once, the probability of the event that the sum of the integers coming on the upper sides of the two dice is 9 is (a) 7/18 (b) 5/36 (c) 1/9 (d) 1/6 30. The probability of getting number 5 in throwing a die is (a) 1 (b) 1/3 (c) 1/6 (d) 5/6 31. The probability of getting a number greater than 2 in throwing a die is (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6 32. The chance of throwing at least 9 in a single throw with two dice, is (a) (b) (c) (d) 33. The probability that the three cards drawn from a pack of 52 cards are all red is (a) (b) (c) (d) 34. The probability of getting a total of 5 or 6 in a single throw of 2 dice is (a) 1/2 (b) 1/4 (c) 1/3 (d) 1/6 35. If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee (a) (b) (c) (d) 666/8436 36. The chance of getting a doublet with 2 dice is (a) (b) (c) (d) 37. A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is (a) (b) (c) (d) 38. Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is (a) 1/9 (b) 1/3 (c) 1/4 (d) 5/9 39. The probability of happening of an impossible event i.e., is (a) 1 (b) 0 (c) 2 (d) – 1 40. For any event A (a) (b) (c) (d) 41. A bag contains 3 red, 4 white and 5 black balls. Three balls are drawn at random. The probability of being their different colours is (a) 3/11 (b) 2/11 (c) 8/11 (d) None of these 42. Find the probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 (while repetition of digit is allowed) (a) (b) (c) (d) None of these 43. If then (a) 1.5 (b) 1.2 (c) 0.8 (d) None of these 44. If four persons are chosen at random from a group of 3 men, 2 women and 4 children. Then the probability that exactly two of them are children, is (a) 10/21 (b) 8/63 (c) 5/21 (d) 9/21 45. A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is (a) 2/11 (b) 3/11 (c) 4/11 (d) 0 46. The probability of three persons having the same date and month for the birthday is (a) 1/365 (b) 1/(365)2 (c) 1/(365)3 (d) None of these 47. Out of 20 consecutive positive integers, two are chosen at random, the probability that their sum is odd is (a) 1/20 (b) 10/19 (c) 19/20 (d) 9/19 48. A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is (a) 1/25 (b) 24/25 (c) 2/25 (d) None of these 49. If E and F are events with and , then (a) Occurrence of E occurrence of F (b) Occurrence of F occurrence of E (c) Non-occurrence of E non-occurrence of F (d) None of the above implications holds 50. A single letter is selected form the word ‘KURUKSHETRA UNIVERSITY’ the probability that it is a vowel is (a) 4/5 (b) 3/7 (c) 8/21 (d) 2/5 51. From the word ‘POSSESSIVE’, a letter is chosen at random. The probability of it to be S is (a) (b) (c) (d) 52. Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is (a) (b) (c) (d) None of these 53. Two dice are tossed. The probability that the total score is a prime number is (a) (b) (c) (d) None of these 54. A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is choosen at random. The probability that this pencil is not defective is (a) 3/5 (b) 3/10 (c) 4/5 (d) 1/2 55. 7 white balls and 3 black balls are placed in a row at random. The probability that no two black balls are adjacent is (a) (b) (c) (d) 56. Twenty children are standing in a line outside a ticket window at Appu Ghar in New Delhi. Ten of these children have a one-rupee coin each and the remaining 10 have a two-rupee coin each. The entry ticket is priced Re. 1. If all the arrangements of the 20 children are equally likely, the probability that the 10th will be the first to wait for change is (Assume that the cashier has no change to begin with) (a) (b) (c) 0 (d) None of these 57. 4 five-rupee coins, 3 two-rupee coins and 2 one-rupee coins are stacked together in a column at random. The probability that the coins of the same denomination are consecutive is (a) (b) (c) (d) None of these 58. Two small squares on a chess board are chosen at random. Probability that they have a common side is (a) 1/3 (b) 1/9 (c) 1/18 (d) None of these 59. There are n persons ( ), among whom are A and B, who are made to stand in a row in random order. Probability that there is exactly one person between A and B is (a) (b) (c) (d) None of these 60. If m rupee coins and n ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins is (a) (b) (c) (d) 61. Twelve balls are distributed among three boxes. The probability that the first box contains 3 balls is (a) (b) (c) (d) 62. Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternately (a) 1/462 (b) 1/924 (c) 1/2 (d) None of these 63. Word ‘UNIVERSITY’ is arranged randomly. Then the probability that both ‘I’ does not come together, is (a) (b) (c) (d) 64. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals (a) 1/2 (b) 1/32 (c) 31/32 (d) 1/5 65. A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is (a) (b) (c) (d) None of these 66. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is (a) 25/39 (b) 14/39 (c) 5/13 (d) 10/13 67. Two numbers are selected at random from 1, 2, 3......100 and are multiplied, then the probability correct to two places of decimals that the product thus obtained is divisible by 3, is (a) 0.55 (b) 0.44 (c) 0.22 (d) 0.33 68. Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6, and 8. What is the probability that they have even digits at both the ends (a) 2/7 (b) 3/7 (c) 4/7 (d) None of these 69. The corners of regular tetrahedrons are numbered 1, 2, 3, 4. Three tetrahedrons are tossed. The probability that the sum of upward corners will be 5 is (a) 5/24 (b) 5/64 (c) 3/32 (d) 3/16 70. If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is (a) 1/8 (b) 2/21 (c) 1/32 (d) 1/35 71. In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a student is selected at random and is found to be studying Mathematics, the probability that the student is a girl, is (a) (b) (c) (d) 72. There are m persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together, is (a) (b) (c) (d) None of these 73. If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form is divisible by 5 equals (a) (b) (c) (d) 74. Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn, then , where is (a) (b) (c) (d) 75. A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the trial is (a) (b) (c) (d) None of these 76. Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals (a) 1/2 (b) 7/15 (c) 2/15 (d) 1/3 77. A committee consists of 9 experts taken from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is (a) (b) (c) (d) 78. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. The probability that only two tests are needed is (a) 1/3 (b) 1/6 (c) 1/2 (d) 1/4 79. A five digit number is formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4 is (a) 3/5 (b) 18/5 (c) 1/5 (d) 6/5 80. Five persons entered the lift cabin on the ground floor of an 8-floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all five persons leaving at different floors is (a) (b) (c) (d) 1 81. If A and B are two events than the value of the determinant choosen at random from all the determinants of order 2 with entries 0 or 1 only is positive or negative respectively. Then (a) (b) (c) (d) None of these 82. are fifty real numbers such that for . Five numbers out of these are picked up at random. The probability that the five numbers have as the middle number is (a) (b) (c) (d) None of these 83. A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 black cards are drawn is (a) (b) (c) (d) None of these 84. An even number of cards is drawn from a pack of 52 cards. The probability that half of these cards will be red and the other half black is (a) (b) (c) (d) 85. Two numbers a and b are chosen at random from the set {1, 2, 3,.....,3n} the probability that is divisible by 3 is (a) (b) (c) (d) None of these 86. The probability that the birth days of six different persons will fall in exactly two calendar months is (a) (b) (c) (d) 87. A bag contains n white and n red balls. Pairs of balls are drawn without replacement until the bag is empty. The probability of each pair consisting of balls of different colours is (a) (b) (c) (d) 1 88. To avoid detection at customs, a traveller has placed six narcotic tablets in a bottle containing nine vitamin pills that are similar in appearance. If the customs official selects three of the tablets at random for analysis, the probability that traveller will be arrested for illegal possession of narcotics is (a) (b) (c) (d) 89. Six different balls are put in three different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is (a) 3/10 (b) 1/6 (c) 1/5 (d) None of these 90. A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of woman's selection is 1/3. What is the probability that none of them will be selected (a) 1/2 (b) 1/12 (c) 1/4 (d) None of these 91. Three six faced unbiased dice are thrown together. The probability that exactly two of the three numbers are equal is (a) 117/216 (b) 5/12 (c) 165/216 (d) None of these 92. If the papers of 4 students can be checked by any one of the seven teachers, then the probability that all the four papers are checked by exactly two teachers is (a) 2/7 (b) 12/49 (c) 32/343 (d) None of these 93. m boys and m girls take their seats randomly around a circle. The probability of their sitting is when (a) No two boys sit together (b) No two girls sit together (c) Boys and girls sit alternatively (d) All the boys sit together 94. m men and w women seat themselves at random on seats arranged in row (circle). If denote the probability of all women sitting together when they are arranged in row (circle), then (a) (b) (c) if and only if (d) if 95. Three player A, B and C, toss a coin cyclically in that order (that is A, B, C, A, B, C, A, B,....) till a head shows. Let p be the probability that the coin shows a head. Let and be, respectively, the probabilities that and C gets the first head. Then (a) (b) (c) (d) 96. Two players A and B toss a fair coin cyclically in the following order till a head shows (that is, A will be allowed first two tosses, followed by a single toss of B). Let denote the probability that gets the head first. Then (a) (b) (c) (d) 97. Three political parties are contesting election for Lok Sabha seats. the probability that there will be a coalition government after the election is (a) (b) (c) (d) 1 98. A and B each throw a dice. The probability that A’s throw is not greater than B’s is (a) 1/6 (b) 5/12 (c) 1/2 (d) 7/12 99. A binary operation is chosen at random from the set of all binary operations on a set A containing n elements. The probability that the binary operation is commutative is (a) (b) (c) (d) None of these 100. Let a die is loaded in such a way that even faces are twice as likely to occur as the odd faces. The probability that a prime number will show up when the die is tossed is (a) (b) (c) (d) 101. A special die with numbers and 3 is thrown thrice. The probability that the total is zero is (a) (b) (c) (d) None of these 102. If four small squares are chosen at random on a chess board, the probability that they lie on a diagonal line is (a) (b) (c) (d) 103. A letter is taken at random out of each of the words CHOICE and CHANCE. The probability that they should be the same letter is (a) 1/6 (b) 1/9 (c) 5/36 (d) 1/324 104. Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is (a) (b) (c) (d) 105. A four figure number is formed of the figures 1, 2, 3, 5 with no repetitions. The probability that the number is divisible by 5 is (a) 3/4 (b) 1/4 (c) 1/8 (d) None of these 106. An elevator starts with m passengers and stops at n floors . The probability that no two passengers alight at the same floor is (a) (b) (c) (d) 107. If ten objects are distributed at random among ten persons, the probability that at least one of them will not get any thing is (a) (b) (c) (d) None of these 108. Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is (a) (b) (c) (d) None of these 109. Five different objects are distributed randomly in 5 places marked 1, 2, 3, 4, 5. One arrangement is picked at random. The probability that in the selected arrangement, none of the object occupies the place corresponding to its number, is (a) 119/120 (b) 1/15 (c) 11/30 (d) None of these 110. 4 gentlemen and 4 ladies take seats at random round a table. The probability that they are sitting alternately is (a) (b) (c) (d) 111. Let . The index n is given a positive integral value at random. The probability that the value of x will have 3 in the units place is (a) (b) (c) (d) None of these 112. There are 7 seats in a row. Three persons take seats at random. The probability that the middle seat is always occupied and no two persons are consecutive is (a) (b) (c) (d) None of these 113. 10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is (a) (b) (c) (d) 114. The probability that out of 10 persons, all born in April, at least two have the same birthday is (a) (b) (c) (d) None of these 115. A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is (a) (b) (c) (d) None of these 116. Three different numbers are selected at random from the set . The probability that the product of two of the numbers is equal to the third is (a) (b) (c) (d) None of these 117. A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle is (a) (b) (c) (d) None of these 118. Let A and B are two independent events. The probability that both A and B occur together is 1/6 and the probability that neither of them occurs is 1/3. The probability of occurrence of A is (a) 0 or 1 (b) 1/2 or 1/3 (c) 1/2 or 1/4 (d) 1/3 or 1/4 119. For an event, odds against is 6 : 5. The probability that event does not occur, is (a) (b) (c) (d) 120. An event has odds in favour 4 : 5, then the probability that event occurs, is (a) (b) (c) (d) 121. A card is drawn from a pack of 52 cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet (a) 17 : 52 (b) 52 : 17 (c) 9 : 4 (d) 4 : 9 122. The odds in favour of a certain event are 2 : 5 and odds against of another event are 5 : 6. If the events are independent, then the probability of happening of at least one of them is (a) 50/77 (b) 51/77 (c) 52/77 (d) 53/77 123. In a horse race the odds in favour of three horses are 1 : 2, 1 : 3 and 1 : 4. The probability that one of the horse will win the race is (a) (b) (c) (d) 124. Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years is (a) 59/91 (b) 44/91 (c) 51/91 (d) 32/91 125. One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are (a) 2 : 3 (b) 1 : 3 (c) 3 : 1 (d) 3 : 2 126. If a party of n persons sit at a round table, then the odds against two specified individuals sitting next to each other are (a) (b) (c) (d) 127. If odds against solving a question by three students are 2 : 1, 5 : 2 and 5 : 3 respectively, then probability that the question is solved only by one student is (a) 31/56 (b) 24/56 (c) 25/56 (d) None of these 128. Odds in favour of an event A are 2 to 1 and odds in favour of are 3 to 1. Consistent with this information the smallest and largest values for the probability of event B are given by (a) (b) (c) (d) None of these 129. The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are (a) (b) (c) (d) None of these 130. If A and B are two mutually exclusive events, then (a) (b) (c) (d) 131. If A and B are two events such that and , then (a) (b) (c) (d) 132. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is (a) 5/108 (b) 18/108 (c) 30/108 (d) 48/108 133. The probability that a leap year will have 53 Fridays or 53 Saturdays is (a) 2/7 (b) 3/7 (c) 4/7 (d) 1/7 134. A box contains 10 good articles and 6 with defects. One article is chosen at random. What is the probability that it is either good or has a defect (a) 24/64 (b) 40/64 (c) 49/64 (d) 64/64 135. The probabilities of occurrence of two events are respectively 0.21 and 0.49. The probability that both occurs simultaneously is 0.16. Then the probability that none of the two occurs is (a) 0.30 (b) 0.46 (c) 0.14 (d) None of these 136. A bag contains 30 balls numbered from 1 to 30, one ball is drawn randomly. The probability that number on the ball is multiple of 5 or 7 is (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4 137. If and then x = (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6 138. If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is (a) 0.5 (b) 0.44 (c) 0.6 (d) None of these 139. A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is (a) 1/52 (b) 1/26 (c) 1/18 (d) None of these 140. If A and B are two independent events, then = (a) (b) (c) (d) 141. In two events , , then A and B are (a) Independent (b) Mutually exclusive (c) Mutually exhaustive (d) Dependent 142. The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then is (a) 2/5 (b) 4/5 (c) 6/5 (d) 7/5 143. If A and B are arbitrary events, then (a) (b) (c) (d) None of these 144. If and then events A and B are (a) Mutually exclusive (b) Independent as well as mutually exhaustive (c) Independent (d) Dependent only on A 145. A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is a black or red ball is (a) 1/3 (b) 1/4 (c) 5/12 (d) 2/3 146. A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart (a) (b) (c) (d) 147. The chance of India winning toss is 3/4. If it wins the toss, then its chance of victory is 4/5 otherwise it is only 1/2. Then chance of India's victory is (a) 1/5 (b) 3/5 (c) 3/40 (d) 29/40 148. Let A and B be events for which P(A) = x, then equals (a) (b) (c) y – z (d) 149. A and B are two events such that , and then (a) 0.1 (b) 0.3 (c) 0.5 (d) None of these 150. A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is (a) 1/13 (b) 1/26 (c) 1/2 (d) 7/13 151. If and the events A and B are mutually exclusive, then x = (a) 3/10 (b) 1/2 (c) 2/5 (d) 1/5 152. One card is drawn randomly from a pack of 52 cards, then the probability that it is a king or spade is (a) 1/26 (b) 3/26 (c) 4/13 (d) 3/13 153. The chance of throwing a total of 7 or 12 with 2 dice, is (a) (b) (c) (d) 154. The probability of three mutually exclusive events A, B and C are given by 2/3, 1/4 and 1/6 respectively. The statement (a) Is true (b) False (c) Nothing can be said (d) Could be either 155. If are any n events, then (a) (b) (c) (d) None of these 156. In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class, has passed in only one subject is (a) 13/25 (b) 3/25 (c) 17/25 (d) 8/25 157. A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing single event is (a) 0.56 (b) 0.54 (c) 0.38 (d) 0.94 158. The chances of throwing a total of 3 or 5 or 11 with two dice is (a) 5/36 (b) 1/9 (c) 2/9 (d) 19/36 159. In a box there are 2 red, 3 black and 4 white balls. Out of these three balls are drawn together. The probability of these being of same colour is (a) (b) (c) (d) None of these 160. A card is drawn at random from a well shuffled pack of 52 cards. The probability of getting a two of heart or diamond is (a) (b) (c) (d) None of these 161. A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is (a) (b) (c) (d) 162. A and B toss a coin alternately, the first to show a head being the winner. If A starts the game, the chance of his winning is (a) 5/8 (b) 1/2 (c) 1/3 (d) 2/3 163. If A and B are two events, then the probability of the event that at most one of A, B occurs, is (a) (b) (c) (d) All of these 164. Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it (a) (b) (c) (d) None of these 165. The probability of hitting a target by three marksmen are and respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is (a) (b) (c) (d) None of these 166. If A speaks truth in 75% cases and B in 80% cases, then the probability that they contradict each other in stating the same statement, is (a) (b) (c) (d) 167. The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is (a) (b) (c) (d) 168. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls. One ball is drawn at random. Then the probability that 2 white and 1 black ball will be drawn (a) 13/32 (b) 1/4 (c) 1/32 (d) 3/16 169. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II, III are p, q and 1/2 respectively. If the probability that the student is successful is 1/2, then (a) (b) (c) (d) There are infinite values of p, q 170. A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is (a) (b) (c) (d) 171. The probability of A, B, C solving a problem are respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is (a) (b) (c) (d) 172. The two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is (a) 0.39 (b) 0.25 (c) 0.904 (d) None of these 173. A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges (a) 24/144 (b) 56/144 (c) 68/144 (d) 76/144 174. A, B, C are any three events. If denotes the probability of S happening then (a) (b) (c) (d) None of these 175. If A and B are any two events, then the probability that exactly one of them occur is (a) (b) (c) (d) 176. If A and B are any two events, then (a) (b) (c) (d) 177. If A and B are any two events, then the true relation is (a) is not less than (b) is not greater than (c) (d) 178. A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is (a) (b) (c) (d) 179. If and then is equal to (a) 0.61 (b) 0.39 (c) 0.48 (d) None of these 180. Suppose that A, B, C are events such that , then (a) 0.125 (b) 0.25 (c) 0.375 (d) 0.5 181. For any two independent events and is (a) (b) (c) (d) None of these 182. Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart (a) (b) (c) (d) None of these 183. If and then (a) 0.3 (b) 0.5 (c) 0.7 (d) 0.9 184. If A and B are two independent events such that and , then (a) (b) (c) (d) 185. If A and B are two independent events such that = 0.40, , then P (neither A nor B) is equal to (a) 0.90 (b) 0.10 (c) 0.2 (d) 0.3 186. The probability of India winning a test match against West Indies is . Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test is (a) (b) (c) (d) 187. A box contains 3 white and 2 red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is (a) (b) (c) (d) 188. The probability of solving a question by three students are respectively. Probability of question is being solved will be (a) (b) (c) (d) 189. Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys, one girl and 3 boys. One child is selected at random from each group. The chance that three selected consisting of 1 girl and 2 boys, is] (a) (b) (c) (d) None of these 190. A, B, C are three events for which and . If then the interval of values of is (a) [0.2, 0.35] (b) [0.55, 0.7] (c) [0.2, 0.55] (d) None of these 191. A student has to match three historical events-Dandi March, Quit India Movement and Mahatma Gandhi's assassination with the years 1948, 1930 and 1942. The student has no knowledge of the correct answers and decides to match the events and years randomly. Let denote the event that the student gets exactly i correct answers. Then (a) (b) (c) (d) 192. Given that A, B and C are events such that and . The probability that at least one of the events A, B or C occurs is (a) (b) (c) (d) 1 193. Suppose that a die (with faces marked 1 to 6) is loaded in such a manner that for K = 1, 2, 3…., 6, the probability of the face marked K turning up when die is tossed is proportional to K. The probability of the event that the outcome of a toss of the die will be an even number is equal to (a) (b) (c) (d) 194. An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is (a) 1/2 (b) 2/5 (c) 1/5 (d) 2/3 195. For the three events and ; P(exactly one of the events A or B occurs) = P (exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where . Then the probability of at least one of the three events A, B and C occurring is (a) (b) (c) (d) 196. A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is (a) (b) (c) (d) None of these 197. Two cards are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is (a) (b) (c) (d) 198. A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these in an ace, is (a) (b) (c) (d) 199. From a pack of 52 cards, two cards are drawn one by one without replacement. The probability that first drawn card is king and second is queen, is (a) (b) (c) (d)